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Homework Help: 2 DOF vibrations mixed system

  1. Aug 20, 2014 #1
    I am struggling with the following question, it is a mixed (lever and linear) 2DOF vibration problem, something I never came across before. I am afraid I am missing something on the FBD, thus the differential equations of motions are wrong.

    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution

    Attached Files:

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  3. Aug 20, 2014 #2


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    You did the right things to set up the equations of motion, but what are the horizontal displacements of the springs ##k_1## and ##k_2##?

    They are not attached at a distance ##L## from the pivot, so they are not ##L\theta##.

    Also, be careful with the signs. You have the amount of stretch in ##k_1## as ##L\theta +x## in one equation and ##L\theta -x## in the other. They can't both be right!
  4. Aug 20, 2014 #3
    I see, distance L for each spring is given in question, is it k2 (L/4)θ+x and k1(L/2)θ ?

    In which case the differential equation of motion become (now with correct signs)
    Iθ + k2 (L/4)θ+x - k1(L/2)θ =0
    mx - k2 (L/4)θ+x =0
  5. Aug 20, 2014 #4


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    The L/2 and L/4 are right.

    With θ and x defined as in the diagram in the question, (L/4)θ and x are both positive to the right. So, is the extension of the spring (L/4)θ+x or (L/4)θ-x ?
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